Draw_a_simulated_data_set: Draw a simulated dataset from model distributions with...

In BayesianFROC: FROC Analysis by Bayesian Approaches

Description

Draw a simulated dataset from model distributions with specified parameters from priors

Usage

Draw_a_simulated_data_set(
  sd = 5,
  C = 5,
  seed.for.drawing.a.prior.sample = 1111,
  fun = stats::var,
  NI = 259,
  NL = 259,
  initial.seed.for.drawing.a.data = 1234,
  ModifiedPoisson = FALSE,
  ite = 1111
)

Arguments

sd	Standard Deviation of priors
C	No. of Confidence levels
seed.for.drawing.a.prior.sample	seed
fun	An one dimensional real valued function defined on the parameter space. This is used in the definition of the rank statistics. Generally speaking, the element of the parameter space is a vector, so the function should be defined on vectors. In my model parameter is mean, standard deviation, C thresholds of the latent Gaussian, so this function should be defined on the C+2 dimensional Euclidean space.
NI	No. of images
NL	No. of Lesions
initial.seed.for.drawing.a.data	seed
ModifiedPoisson	Logical, that is TRUE or FALSE. If ModifiedPoisson = TRUE, then Poisson rate of false alarm is calculated per lesion, and a model is fitted so that the FROC curve is an expected curve of points consisting of the pairs of TPF per lesion and FPF per lesion. Similarly, If ModifiedPoisson = TRUE, then Poisson rate of false alarm is calculated per image, and a model is fitted so that the FROC curve is an expected curve of points consisting of the pair of TPF per lesion and FPF per image. For more details, see the author's paper in which I explained per image and per lesion. (for details of models, see vignettes , now, it is omiited from this package, because the size of vignettes are large.) If ModifiedPoisson = TRUE, then the False Positive Fraction (FPF) is defined as follows (F_c denotes the number of false alarms with confidence level c ) \frac{F_1+F_2+F_3+F_4+F_5}{N_L}, \frac{F_2+F_3+F_4+F_5}{N_L}, \frac{F_3+F_4+F_5}{N_L}, \frac{F_4+F_5}{N_L}, \frac{F_5}{N_L}, where N_L is a number of lesions (signal). To emphasize its denominator N_L, we also call it the False Positive Fraction (FPF) per lesion. On the other hand, if ModifiedPoisson = FALSE (Default), then False Positive Fraction (FPF) is given by \frac{F_1+F_2+F_3+F_4+F_5}{N_I}, \frac{F_2+F_3+F_4+F_5}{N_I}, \frac{F_3+F_4+F_5}{N_I}, \frac{F_4+F_5}{N_I}, \frac{F_5}{N_I}, where N_I is the number of images (trial). To emphasize its denominator N_I, we also call it the False Positive Fraction (FPF) per image. The model is fitted so that the estimated FROC curve can be ragraded as the expected pairs of FPF per image and TPF per lesion (ModifiedPoisson = FALSE ) or as the expected pairs of FPF per image and TPF per lesion (ModifiedPoisson = TRUE) If ModifiedPoisson = TRUE, then FROC curve means the expected pair of FPF per lesion and TPF. On the other hand, if ModifiedPoisson = FALSE, then FROC curve means the expected pair of FPF per image and TPF. So,data of FPF and TPF are changed thus, a fitted model is also changed whether ModifiedPoisson = TRUE or FALSE. In traditional FROC analysis, it uses only per images (trial). Since we can divide one image into two images or more images, number of trial is not important. And more important is per signal. So, the author also developed FROC theory to consider FROC analysis under per signal. One can see that the FROC curve is rigid with respect to change of a number of images, so, it does not matter whether ModifiedPoisson = TRUE or FALSE. This rigidity of curves means that the number of images is redundant parameter for the FROC trial and thus the author try to exclude it. Revised 2019 Dec 8 Revised 2019 Nov 25 Revised 2019 August 28
ite	A variable to be passed to the function rstan::sampling() of rstan in which it is named iter. A positive integer representing the number of samples synthesized by Hamiltonian Monte Carlo method, and, Default = 1111

Value

A single synthesized data-set

Examples

## Not run: 
   one.dataList  <-  Draw_a_simulated_data_set()


## End(Not run)# dottest

BayesianFROC documentation built on Jan. 23, 2022, 9:06 a.m.